U.S. patent application number 12/741370 was filed with the patent office on 2011-01-27 for methods and apparatus for measuring the contents of a search volume.
This patent application is currently assigned to MICRIMA LIMITED. Invention is credited to Ralph Benjamin, Ian James Craddock, Maciej Bartlomiej Klemm.
Application Number | 20110022325 12/741370 |
Document ID | / |
Family ID | 38834852 |
Filed Date | 2011-01-27 |
United States Patent
Application |
20110022325 |
Kind Code |
A1 |
Craddock; Ian James ; et
al. |
January 27, 2011 |
Methods and Apparatus for Measuring the Contents of a Search
Volume
Abstract
A method of measuring the contents of a search volume. The
method includes: energising one or more transmitters so as to
transmit electromagnetic wave energy into the search volume;
detecting the effect of the search volume on the passage of the
electromagnetic wave energy by recording two or more signals, each
signal being associated with a different propagation path
(typically either a monostatic or bistatic path) within the search
volume; aligning the signals in order to generate two or more
aligned signals which are synthetically focused on a desired voxel
in the search volume, each aligned signal being associated with a
different propagation path (typically either a monostatic or
bistatic path) within the search volume; calculating a quality
factor by processing the aligned signals to generate two or more
data values, and processing the data values to generate a quality
factor, the quality factor being indicative of a degree of
coherence in the aligned signals; summing the aligned signals to
generate a summed signal; and processing the summed signal to
generate an output which is indicative of the internal structure of
the search volume at the location of the desired voxel, the output
varying in accordance with the quality factor.
Inventors: |
Craddock; Ian James;
(Bristol, GB) ; Klemm; Maciej Bartlomiej;
(Bristol, GB) ; Benjamin; Ralph; (Bristol,
GB) |
Correspondence
Address: |
MARSHALL, GERSTEIN & BORUN LLP
233 SOUTH WACKER DRIVE, 6300 WILLIS TOWER
CHICAGO
IL
60606-6357
US
|
Assignee: |
MICRIMA LIMITED
Bristol
GB
|
Family ID: |
38834852 |
Appl. No.: |
12/741370 |
Filed: |
November 4, 2008 |
PCT Filed: |
November 4, 2008 |
PCT NO: |
PCT/GB2008/003721 |
371 Date: |
October 15, 2010 |
Current U.S.
Class: |
702/19 ;
702/71 |
Current CPC
Class: |
A61B 5/0507 20130101;
G01S 13/89 20130101; A61B 5/05 20130101 |
Class at
Publication: |
702/19 ;
702/71 |
International
Class: |
G06F 19/00 20060101
G06F019/00; G01R 29/00 20060101 G01R029/00 |
Foreign Application Data
Date |
Code |
Application Number |
Nov 5, 2007 |
GB |
0721694.8 |
Claims
1. A method of measuring the contents of a search volume, the
method including: energising one or more transmitters so as to
transmit electromagnetic wave energy into the search volume;
detecting the effect of the contents of the search volume on the
passage of the electromagnetic wave energy by recording two or more
signals, each signal being associated with a different propagation
path within the search volume; aligning the signals in order to
generate two or more aligned signals which are synthetically
focused on a desired voxel in the search volume, each aligned
signal being associated with a different propagation path within
the search volume; calculating a quality factor by processing the
aligned signals to generate two or more data values, and processing
the data values to generate the quality factor, the quality factor
being indicative of a degree of coherence in the aligned signals;
summing the aligned signals to generate a summed signal; and
processing the summed signal to generate an output which is
indicative of the contents of the search volume at the location of
the desired voxel, the output varying in accordance with the
quality factor.
2. The method of claim 1 where each data value is indicative of the
energy of one or more of the aligned signals.
3. The method of claim 1 wherein the step of calculating the
quality factor includes calculating a parameter which is indicative
of a degree of statistical dispersion of the data values.
4. The method of claim 1 wherein the step of calculating the
quality factor includes calculating a parameter which assesses the
total energy of the summed signal relative to the sum of all the
energies of the aligned signals.
5. The method of claim 4 wherein the energies are computed from
only part of the signal bandwidth.
6. The method of claim 1 wherein the step of calculating the
quality factor includes generating a series of different summed
signals, each different summed signal being generated by summing a
different number of the aligned signals; processing the different
summed signals to generate a series of different data values; and
fitting a curve to the different data values.
7. The method of claim 6 where a different result can be achieved
by changing the order of the summation.
8. The method of claim 6 wherein the curve is a polynomial
curve.
9. The method of claim 8 wherein the summed signals are
proportional to energy and the curve is a quadratic curve.
10. The method of claim 1 wherein the signals recorded in step b)
are equalised signals.
11. The method of claim 1 wherein step a) comprises sequentially
energising two or more transmitters.
12. The method of claim 11 wherein step b) comprises sequentially
recording two or more signals, each signal being associated with a
different propagation path within the search volume.
13. The method of claim 1 wherein the search volume is part of a
human or animal body.
14. The method of claim 4 wherein the quality factor is calculated
by summing the aligned signals; generating a first energy data
value from the summed signal; summing the energies of the aligned
signals to generate a second energy data value, and calculating the
ratio between the two energy data values.
15. The method of claim 1 wherein the signals recorded in step b)
are pre-processed signals.
16. Apparatus for measuring the contents of a search volume, the
apparatus comprising: an antenna array configured to transmit and
receive electromagnetic wave energy to and from the search volume;
and a processor configured to: record two or more signals, each
signal being indicative of the effect of the search volume on the
passage of the electromagnetic wave energy and being associated
with a different propagation path within the search volume, align
the signals in order to generate two or more aligned signals which
are synthetically focused on a desired voxel in the search volume,
each aligned signal being associated with a different propagation
path within the search volume; calculate a quality factor by
processing the time-aligned signals to generate two or more data
values, and processing the data values to generate the quality
factor, the quality factor being indicative of a degree of
coherence in the aligned signals; sum the aligned signals to
generate a summed signal; and process the summed signal to generate
an output which is indicative of the contents of the search volume
at the location of the desired voxel, the output varying in
accordance with the quality factor.
Description
FIELD OF THE INVENTION
[0001] The present invention relates to a method and apparatus for
measuring the contents of a search volume using electromagnetic
wave energy.
BACKGROUND OF THE INVENTION
[0002] A method of measuring the contents of a search volume using
electromagnetic energy is described in U.S. Pat. No. 5,920,285.
Individual transmit elements of a transmit array are actuated in
turn in order to interrogate the search volume. Reflected signals
are recorded, and appropriate phase or time shifts are inserted to
simulate, post reception, the shifts that would have occurred if
either or both of the transmit and receive array had been focused
on the cell using phased array beam steering techniques.
[0003] Another method of measuring the contents of a search volume
is described in WO 2006/085052 A2. The method includes the steps
of: energising one or more transmitters so as to transmit
electromagnetic wave energy into the search volume; detecting the
effect of the search volume on the passage of the electromagnetic
wave energy by recording two or more signals at one or more
receivers, each signal being associated with a different
transmitter/receiver pair; pre-processing the signals to generate
two or more pre-processed signals, each pre-processed signal being
associated with a different transmitter/receiver pair; aligning the
pre-processed signals in order to generate two or more aligned
signals which are synthetically focused on a desired voxel in the
search volume, each aligned signal being associated with a
different transmitter/receiver pair; and summing the aligned
signals to generate an output which is indicative of the internal
structure of the search volume at the location of the desired
voxel.
[0004] Various methods of removing skin surface artefacts are
described in WO 2006/085052 A2. However these methods are not
effective in removing clutter caused by other effects. These
effects include single and multiple reflections from parts of the
antenna, its feed, the array structure and the body.
SUMMARY OF THE INVENTION
[0005] A first aspect of the invention provides a method of
measuring the contents of a search volume, the method including:
[0006] a) energising one or more transmitters so as to transmit
electromagnetic wave energy into the search volume; [0007] b)
detecting the effect of the search volume on the passage of the
electromagnetic wave energy by recording two or more signals, each
signal being associated with a different propagation path
(typically either a monostatic or bistatic path) within the search
volume; [0008] c) aligning the signals in order to generate two or
more aligned signals which are synthetically focused on a desired
voxel in the search volume, each aligned signal being associated
with a different propagation path (typically either a monostatic or
bistatic path) within the search volume; [0009] d) calculating a
quality factor by processing the aligned signals to generate two or
more data values, and processing the data values to generate a
quality factor, the quality factor being indicative of a degree of
coherence in the aligned signals; [0010] e) summing the aligned
signals to generate a summed signal; and [0011] f) processing the
summed signal to generate an output which is indicative of the
internal structure of the search volume at the location of the
desired voxel, the output varying in accordance with the quality
factor.
[0012] The signals which are recorded in step b) and aligned in
step c) of the method may comprise raw measured data--that is,
unprocessed signals direct from the antennae. Alternatively they
may be pre-processed signals which have been pre-processed in some
way--for example to reduce or remove unwanted background signals in
the raw measured data.
[0013] A second aspect of the invention provides apparatus for
measuring the contents of a search volume, the apparatus including:
[0014] a) an antenna array configured to transmit and receive
electromagnetic wave energy to and from the search volume; and
[0015] b) a processor configured to: [0016] i) record two or more
signals, each signal being indicative of the effect of the search
volume on the passage of the electromagnetic wave energy and being
associated with a different propagation path within the search
volume, [0017] ii) align the signals in order to generate two or
more aligned signals which are synthetically focused on a desired
voxel in the search volume, each aligned signal being associated
with a different propagation path within the search volume; [0018]
iii) calculate a quality factor by processing the time-aligned
signals to generate two or more data values, and processing the
data values to generate the quality factor, the quality factor
being indicative of a degree of coherence in the aligned signals;
[0019] iv) sum the aligned signals to generate a summed signal; and
[0020] v) process the summed signal to generate an output which is
indicative of the internal structure of the search volume at the
location of the desired voxel, the output varying in accordance
with the quality factor.
[0021] The signals which are recorded and aligned by the processor
may comprise raw measured data--that is, unprocessed signals direct
from the antenna array. Alternatively they may be pre-processed
signals which have been pre-processed in some way--for example to
reduce or remove unwanted background signals in the raw measured
data.
[0022] In one embodiment of the invention described below, each
data value is indicative of the energy of one or more of the
aligned signals. However each data value may be indicative of other
properties, such as: [0023] the amplitude of one or more of the
aligned signals; [0024] the amplitude of the spectral content of
one or more of the aligned signals at one or more frequencies;
[0025] the spectral content of one or more of the time-aligned
signals at one or more frequencies; or [0026] the time of arrival
of one or more of the time-aligned signals.
[0027] The step of calculating the quality factor may include
calculating a parameter which is indicative of a degree of
statistical dispersion of the data values. This parameter may be
for example the standard deviation, variance, range, interquartile
range, mean difference, mean absolute deviation, average absolute
deviation, or a similar statistical measure of the dispersion of
any of the above-mentioned data values.
[0028] The step of calculating the quality factor may include
calculating a parameter which assesses the total energy of the
summed signal relative to the sum of all the energies of the
aligned signals. These energies may be computed from the entire
signal or from only part of the signal bandwidth if it is desired
to emphasize a particular band of the signal.
[0029] The step of calculating the quality factor may include
generating a series of different summed signals, each different
summed signal being generated by summing a different number of the
aligned signals; and processing the different summed signals to
calculate the quality factor. For instance the different summed
signals may be processed to generate a series of different data
values (such as energy values); and fitting a curve to the
different data values. This may be performed in combination with
the parameter which is indicative of a degree of statistical
dispersion of the data values, or separately. Note that a different
result may be achieved by changing the order of the summation.
[0030] Typically the curve is a polynomial curve such as a
quadratic curve.
[0031] Typically step a) comprises sequentially energising two or
more transmitters. The two or more signals can then be sequentially
recorded, each signal being associated with a respective one of the
transmitters. Alternatively, simultaneous transmission from two or
more transmitters may be accomplished if desired, by any suitable
multiplexing scheme such as code or frequency multiplexing.
[0032] The antennae may be operated monostatically: that is
transmitting and receiving at the same antenna. Alternatively or
additionally step b) may comprise sequentially or concurrently
recording two or more first signals at a first antenna, each first
signal being associated with a respective one of the transmitters;
and sequentially or concurrently recording two or more second
signals at a second antenna, each second signal being associated
with a respective one of the transmitters.
[0033] Typically the search volume is part of a human or animal
body such as a human breast.
[0034] Note that the various elements of the method are presented
as a series of steps a)-f) but it will be appreciated that these
steps may be performed in any order relative to each other, or at
the same time. For instance step d) may be performed before or
after step e), or at the same time.
[0035] Note also that the various elements of the method are
presented as distinct steps a)-f) but it will be appreciated that
some of these steps may be merged or replaced by an arithmetic
equivalent. For instance instead of summing the aligned signals in
step e) and then multiplying the summed signal in step f) by the
quality factor, the individual aligned signals may each be
multiplied by the quality factor before being summed.
[0036] In the preferred embodiment below, microwave energy is used
to measure the internal structure of a human breast, but in more
general terms any frequency of energy may be used, including
electromagnetic energy at optical frequencies. Examples include
radar imaging of airspace, through-wall radar and imaging of rooms
for security applications. Thus the search volume may comprise a
discrete object (such as part of a human or animal body) or a more
general search volume such as an air or sea space.
BRIEF DESCRIPTION OF THE DRAWINGS
[0037] Various embodiments of the present invention will now be
described with reference to the accompanying drawings, in
which:
[0038] FIG. 1 is a system overview of a breast tumour imaging
system.
[0039] FIG. 2 shows an example of a curve of energy collection data
values.
[0040] FIG. 3 shows detection results for a 10 mm spherical phantom
tumour: a) standard Delay And Sum (DAS), b) improved DAS with
QF=a.
[0041] FIG. 4 shows 2D focusing results for standard and improved
DAS algorithms, for different horizontal planes along the Z-axis:
a) standard DAS, z=-18, b) standard DAS, z=-27, c) improved DAS,
z=-18, d) improved DAS, z=-27. The 2D contour plots of FIG. 4 show
signal energy on a linear scale, normalised to the maximum in the
3D volume.
[0042] FIG. 5 shows curves of energy collection data values at
focal points P.sub.T, P.sub.1 and P.sub.2 (see FIG. 6(a)): a) curve
for P.sub.T as in standard DAS, a) curve for P.sub.i as in standard
DAS, c) curve for P.sub.2 in standard DAS, d) curve for P.sub.T as
in improved DAS together with the polynomial fitted, e) curve for
P.sub.1 in the improved DAS together with the polynomial fitted, f)
curve for P.sub.2 in the improved DAS together with the polynomial
fitted.
[0043] FIG. 6 shows detection results for a 7 mm spherical phantom
tumour: a) standard DAS, b) improved DAS with QF=a. 3D figures
present -3 dB contour map of scattered energy.
[0044] FIG. 7 shows 2D focusing results for standard and improved
DAS algorithms, for different horizontal planes along the Z-axis:
a) standard DAS, z=-9, b) standard DAS, z=-27, c) standard DAS,
z=-33, d) improved DAS, z=-6, e) improved DAS, z=-27, f) improved
DAS, z=-33. The 2D contour plots of FIG. 7 show signal energy on a
linear scale, normalised to the maximum in the 3D volume.
[0045] FIG. 8 shows curves of energy collection data values at
focal points P.sub.T, P.sub.1 and P.sub.2 (see FIG. 6(a)): a) curve
for P.sub.T as in standard DAS, a) curve for P.sub.1 as in standard
DAS, c) curve for P.sub.2 in standard DAS, d) curve for P.sub.T as
in improved DAS together with the polynomial fitted, e) curve for
P.sub.1 in the improved DAS together with the polynomial fitted, f)
curve for P.sub.2 in the improved DAS together with the polynomial
fitted.
DETAILED DESCRIPTION OF EMBODIMENT(S)
[0046] A real aperture synthetically organised radar for breast
cancer detection shown in FIG. 1 operates by employing an array 2
of N antennas (e.g. 3) close to, or in contact with, the breast 1.
Each antenna is energised in turn to transmit a pulse of
electromagnetic wave energy into the breast 1, and the effect of
the breast on the passage of the electromagnetic wave energy is
detected by receiving reflected signals y.sub.i(t) at each of the
other antennas and recording the signals y.sub.i(t). Thus each
signal y.sub.i(t) is associated with an i.sup.th
transmitter/receiver pair of antennas, and consequently with a
different propagation path within the breast 1. The pulse generator
8 and the detector 9 may be time-shared, by means of a switching
matrix 5 as shown in FIG. 1, as may any transmit or receive path
amplification (6, 7).
[0047] The detector 9 includes a processor configured to perform
various signal processing steps described below. The first step of
signal processing deals with the reduction or elimination of
unwanted background signals in the raw measured data. This process
must be performed before equalisation and 3D focusing algorithms
will be applied. When a mono-static synthetic aperture radar is
used for breast cancer detection, tumour extraction aims at
removing strong skin reflection from measured data. This is usually
performed by simple subtraction from the averaged skin reflection
signal (see E. Fear, X. Li, S. C. Hagness, and M. Stuchly,
"Confocal microwave imaging for breast cancer detection:
Localization of tumors in three dimensions," IEEE Transactions on
Biomedical Engineering, vol. 49, no. 8, pp. 812-822, August 2002)
or by more sophisticated algorithms as presented in E. J. Bond, X.
Li, S. C. Hagness, and B. D. Van Veen, "Microwave imaging via
space-time beamforming for early detection of breast cancer," IEEE
Transactions on Antennas and Propagation, vol. 51, no. 8, pp.
1690-1705, August 2003.
[0048] The approach used in the system of FIG. 1 to reduce or
remove unwanted background signals is different. In the
multi-static real aperture array 2, the measured response contains
not only strong skin reflections, but also reflections from other
mechanical parts of the array as well as antenna coupling signals.
All these undesired signals are usually of greater amplitude than
the tumour response. To subtract all unwanted signals, the antenna
array 2 is physically rotated and a second radar measurement is
performed. This target displacement method is commonly used in
radar cross-section measurements to subtract undesired signals. See
for example: [0049] R. A. Man, U. H. W Lammers, T. B. Hansen, T. J.
Tanigawa, R. V. McGahan, "Bistatic RCS Calculations From
Cylindrical Near-Field Measurements--Part II: Experiments", IEEE
Transactions on Antennas and Propagation, Volume 54, Issue 12,
December 2006 Page(s):3857-3864; and [0050] I. J. LaHaie and M. A.
Blischke, "Mitigation of multipath and ground interactions in RCS
measurements using a single target translation", in Proc. 23.sup.rd
Annual Meeting of the Antenna Measurement Techniques Association
(AMTA 01), Denver, Colo., 2001, pp. 411-416.
[0051] Rotation gives two sets of measured data, in which undesired
signals such as antenna coupling, or skin reflections are almost
identical and appear at the same time position, therefore they can
be eliminated. In contrast, a tumour response will appear at
different time positions in these two measured sets (unless it is
on the axis of rotation). Applicability of this technique will
depend on the homogeneity of the breast within a given angle
defined by rotation. It is therefore assumed that within the angle
of array rotation: a) the distance between the antennas 2 and the
skin remains unchanged, b) skin properties and thickness is the
same, c) normal breast tissue properties do not change.
[0052] Before applying the focusing algorithm described below, a
pre-processing step is normally performed. This process aims at
equalisation of scattered tumour responses for different antenna
pairs. Ideal pre-processing would result in all received pulses
being of the same shape, amplitude and perfectly time-aligned. In
pre-processing the following steps are performed: 1. reduction or
elimination of background signals, by subtraction, from measured
data, 2. equalisation of tissue losses, 3. equalisation of radial
spread of the spherical wavefront, 4. removal of skin artefacts as
described in WO 2006/085052 A2. In the description below for
simplicity we do not account for the frequency-dependence of the
tissue losses nor for the frequency-dependent radiation patterns of
the antennas.
[0053] Delay-and-sum (DAS) beamforming is a basic and well known
method. See for example: [0054] Wenyi Shao; Beibei Zhou; Zhaowen
Zheng; Gang Wang; "UWB Microwave Imaging for Breast Tumor Detection
in Inhomogeneous Tissue", 2005. IEEE-EMBS 27th Annual International
Conference of the Engineering in Medicine and Biology Society,
Page(s):1496-1499 [0055] W. Zhisong, L. Jian, W. Renbiao;
"Time-delay- and time-reversal-based robust capon beamformers for
ultrasound imaging", IEEE Transactions on Medical Imaging, Volume
24, Issue 10, October 2005 Page(s):1308-1322.
[0056] First the pre-processing steps described above are
performed, optionally including removal of skin artefacts in step
4. Next, appropriate time-delays T.sub.i for all received signals
are computed. The time-delay T.sub.i for a given
transmitter/receiver pair is calculated based on the antennas'
positions, the position of the focal point r=(x; y; z) as well as
an estimate of average wave propagation speed, which in the present
case is simply assumed to be constant across the band.
[0057] Essentially, the scattered energy at a given focal point
within the breast volume can be expressed as:
F r ( x , y , z ) = .intg. 0 .tau. ( i = 1 M w i ( x , y , z ) y i
( t - T i ( x , y , z ) ) ) 2 t ( 1 ) ##EQU00001## [0058] where:
M=N(N-1)/2 (N is the number of antennas in the array), w.sub.i is a
location dependant weight calculated during pre-processing, y.sub.i
is the measured radar signal; and T.sub.i is the time-delay along
the bistatic path to the location (x, y, z).
[0059] During image formation, the focal point moves from one
position to another within the breast. At each location all
time-shifted responses are coherently summed and integrated.
Integration is performed on the windowed signal, the length of the
integration window being chosen according to the system bandwidth.
A three-dimensional (3D) map of scattered energy is formed in this
way. The main advantage of the DAS algorithm is its simplicity,
robustness and short computation time.
[0060] The improved DAS algorithm uses an additional weighting
factor QF (quality factor), compared to the standard DAS expressed
in equation (1) above. QF can be interpreted as a quality factor of
the coherent focusing algorithm. In one possible implementation it
is calculated in three steps. Firstly, for each focal point, a
curve of cumulative energy collection is plotted during the
coherent signal summation. An example of such a measured curve at a
focal point containing a tumour response is presented in FIG.
2.
[0061] The X-axis of the curve in FIG. 2 represents a respective
value for M in equation (1) above, and the Y-axis represents
F.sub.r(x,y,z) for that value of M. In other words, the first data
value forming the curve (where M=1) represents the energy from one
transmitter/receiver pair only, the mid-point (where M=60)
represents the energy from a sum of the signals from half of the
transmitter/receiver pairs, and the last data value (where M=120)
represents the energy from a full summation of the signals from all
transmitter/receiver pairs. Thus this last data value, obtained
after summation of all radar signals, is equal to the focused
energy F.sub.r(x,y,z) in equation (1) above.
[0062] Next, the energy collection curve of FIG. 2 is re-scaled by
normalising it to the standard deviation of energy, .sigma..sub.e,
for all radar signals used in the summation. Normalisation is
actually performed using multiplication by 1/(1+.sigma..sub.e),
since in the ideal case of equal energy in all (equalised) measured
radar signals .sigma..sub.e=0. This may be thought of as a
heuristic scaling of the data to give greater weight to those
signals that, following equalisation, more closely resemble the
desired case of equal energy. The utility of this heuristic
weighting is evident from the results presented in the following
sections.
[0063] In a last step, the processor estimates the coefficients of
a second-order polynomial (y=ax.sup.2+bx+c), which is the
least-square error fit of the normalised curve of coherent energy
collection. The choice of the second-order polynomial comes from
the fact that a curve of cumulative energy collection during a
perfect coherent signal summation would follow a quadratic curve.
Then, the processor assumes that QF=a.
[0064] The characteristic equation of the improved DAS algorithm
can therefore be expressed as:
F r ( x , y , z ) = QF ( x , y , z ) .intg. 0 .tau. ( i = 1 M w i (
x , y , z ) y i ( t - T i ( x , y , z ) ) ) 2 t ( 2 ) ##EQU00002##
[0065] where: [0066] y, (t) is i.sup.th measured radar signal.
[0067] .tau. is the duration of the integration window, which is
approximately equal to the reciprocal of the bandwidth. [0068]
w.sub.i(x,y,z)y.sub.i(t) is the pre-processed signal associated
with the i.sup.th transmitter/receiver pair at time t; [0069]
w.sub.i(x,y,z)y.sub.i(t-T.sub.i(x,y,z)) is the time-aligned signal
synthetically focused on a desired voxel in the search volume at
position x,y,z at time (t-T.sub.i(x,y,z)) and associated with the
i.sup.th transmitter/receiver pair; and [0070] QF(x,y,z) is the
quality factor calculated by processing the time-aligned signals to
generate a curve of energy data values as shown in FIG. 2, and
processing the curve of energy data values to generate the quality
factor QF, the quality factor QF being indicative of a degree of
coherence in the aligned signals at the position x,y,z.
[0071] Sections A and B below present the experimental results of
tumour detection using a curved antenna array and 3D breast
phantom. Focusing results for standard DAS algorithm are compared
to those for the improved DAS and differences between both
algorithms are discussed. Results are presented for tumours of two
different sizes and located at different positions: a) 10 mm
spherical tumour located at position P.sub.T (x=20, y=20, z=-20),
b) 7 mm spherical tumour located at position P.sub.T (x=20, y=10,
z=-10). All co-ordinates are quoted in mm.
Section A. 10 mm Spherical Phantom Tumour
[0072] FIGS. 3a and 3b present 3D focusing results for a 10 mm
spherical phantom tumour located at the position P.sub.T (x=20,
y=20, z=-20). Specifically, these figures present -3 dB contour
maps of scattered energy, which is assumed to be indicative of the
internal structure of the search volume at the location of the
desired voxel at position x,y,z. FIGS. 3a and 3b contrast the
outputs of the standard DAS algorithm of equation 1 (FIG. 3(a)) and
the improved DAS algorithm of equation 2 (FIG. 3(b)). As can be
seen in FIG. 3(a), there are several scatterers present in the
image when focusing the standard DAS algorithm. The strongest
scatterer within the entire 3D volume is located at position
P.sub.T (x=15, y=18, z=-18) and it is associated with a tumour
response. FIG. 3a also indicates the locations of two other strong
scatterers located at position P.sub.i(x=-21, y=9, z=-18) and
P.sub.2(x=-18, y=-21, z=-27). FIGS. 4(a) and 4(b) present 2D
focusing results for standard. DAS on the horizontal planes
(Z-axis) containing the P.sub.T, P.sub.1 (both at z=-18) and
P.sub.2(z=-27) signals associated with clutter. The 2D contour
plots show signal energy on a linear scale, normalised to the
maximum in the entire 3D volume. The skin location at each plane is
presented as a black circle. From FIG. 4(a) for the plane
containing the tumour the focused tumour response (P.sub.T) can be
relatively easily recognised and the nearby twin tumour response
(at x=18, y=9; the twin target response is due to the background
subtraction method--mechanical array rotation by 10 degrees). FIG.
4a also shows strong clutter at position P.sub.1 and weaker clutter
at other positions arising from imperfect background subtraction.
FIG. 4(b) presents the 2D focusing result through the plane (z=-27)
containing a strong clutter scatterer at P.sub.2.
[0073] Significantly better detection results are obtained using
the improved DAS algorithm presented herein. 3D and 2D focusing
results for the improved DAS are presented in FIG. 3(b) and FIGS.
4(c)-4(d). The 3D contour map of scattered energy shown in FIG. 3b
contains only the tumour response (P.sub.T) and the twin tumour
response. Unlike the image of FIG. 3a obtained using standard DAS,
there are no other clutter scatterers visible. Signal to clutter
ratio, defined as the ratio between energy of the tumour response
to the strongest clutter energy within a single 3-D dataset, was
improved from 1.25 dB for standard DAS to 3.9 dB for improved DAS
(a 2.65 dB improvement).
[0074] The same improved performance is observed in the 2D results
shown in FIGS. 4(c) and 4(d). As shown in FIG. 4c, in the
horizontal plane containing P.sub.T, the tumour response clearly
stands out and very little clutter exists in the image. As shown in
FIG. 4d, in the plane containing P.sub.2, clutter is also
significantly suppressed. The results shown in FIGS. 3 and 4 show
the improved tumour detection of the new DAS algorithm, which uses
an additional weight QF, compared to standard DAS.
[0075] The following section analyses this particular variant of an
improved DAS algorithm and explains why it provides better results.
To do so, we will go through all steps of the new algorithm at the
three focal points (P.sub.T, P.sub.i, P.sub.2) mentioned earlier.
After subtraction of background signals from measured data (by
mechanical array rotation), the resultant signals are pre-processed
and time-aligned. This initial step is identical for the standard
and improved DAS algorithms. Then all pre-processed and
time-aligned signals (120 signals for array 2) are coherently
summed to give 120 scalar energy quantities.
[0076] During this process a curve of cumulative energy collection
data values is obtained, at each focal point within the focusing
volume. This curve is presented in FIG. 5(a), 5(b), 5(c) for focal
points P.sub.T, P.sub.1, P.sub.2, respectively. The data values in
FIGS. 5a-5c are generated in a similar way to the data values shown
in FIG. 2. That is, each data value represents F.sub.r (x,y,z) for
a given value of M. If we assume that the focused energy for the
tumour location P.sub.T using the standard DAS algorithm is equal
to unity F.sub.s(P.sub.T)=1, then the focused energy values at
focal points P.sub.1 and P.sub.2 are F.sub.s(P.sub.1)=0.88 and
F.sub.s(P.sub.2)=0.85 respectively. Next, the improved DAS
algorithm calculates the standard deviation of energy .sigma..sub.e
for all radar signals and re-calculates energy collection curves by
normalising them to .sigma..sub.e. The rationale to do so is based
on the fact that after the initial pre-processing equalisation
step, all radar signals should have similar energy.
[0077] FIGS. 5d-5f (solid curves) show re-scaled (normalised)
curves for locations P.sub.T, P.sub.i, and P.sub.2 respectively. It
can be observed that, after this normalisation, the results have
improved, since the curves for P.sub.1, P.sub.2 have significantly
smaller amplitudes than for P.sub.T. Since clutter signals can not
be thought as totally uncorrelated, we do not however simply use
.sigma..sub.e as the weight factor but apply additional criteria
related to the coherent summation of radar signals, as follows.
[0078] First, it is assumed that in the ideal case the cumulative
energy collection curve should follow a parabola (y=x.sup.2). It
follows a parabola because e.g. if n in-phase unity-amplitude
sinusoids are summed, the resulting sinusoid has an amplitude n.
Since the energy is proportional to the square then the energy
grows with n.sup.2. However a curve containing clutter does not
follow a parabola because the sinusoids will not have the same
phase. For example if n out-of-phase sinusoids are added, the
resulting sinusoid is smaller in amplitude than n. As a further
example, if the n+1.sup.th signal is in anti-phase to the mean of
the previous n signals, it actually results in a reduction of the
cumulative energy, rather than an increment.
[0079] Therefore, to check the `quality` of coherent addition of
radar signals in the system, the processor performs a second-order
polynomial (y=ax.sup.2+bx+c) fitting (in the least-square sense) to
the measured energy collection curves. This process is performed on
the normalised curves. Results of polynomial fitting are shown in
FIGS. 5(d)-5(f) (dashed curve), and the constant a associated with
x.sup.2 equals a=0.167 for P.sub.T, a=0.071 for P.sub.1 and a=0.028
for P.sub.2. Then, assuming that QF=a (see equation 2), the focused
energy using improved DAS in this example is: F.sub.s(P.sub.T)=1,
F.sub.s(P.sub.2)=0.38 and F.sub.s(P.sub.1)=0.14.
Section B. 7 mm Spherical Phantom Tumour
[0080] This section presents the detection of a smaller, 7 mm
spherical tumour phantom. In FIG. 63D focusing results are
presented for a 6 mm spherical phantom tumour located at the
position P.sub.T (x=20, y=10, z=-10). FIGS. 6a and 6b present -3 dB
contour maps of scattered energy, when focusing was performed using
the standard DAS algorithm (FIG. 6(a)) and the improved DAS
algorithm (FIG. 6(b)).
[0081] As can be seen in FIG. 6(a), by using standard DAS algorithm
there are multiple scatterers present in the image. As described
previously in Section A for a 10 mm tumour, again the following
analysis concentrates on three focal points: a spherical phantom
tumour located at P.sub.T (x=21, y=9, z=-6), the strongest clutter
scatterer at P.sub.i (x=-24, y=-15, z=-27) and another strong
clutter at P.sub.2 (x=18, y=-9, z=-33). A significantly better
image, with clearly visible tumour scatterer at P.sub.T and no
other clutter targets, is presented in FIG. 6(b) for the improved
DAS algorithm. Signal to clutter ratio was improved from 0.8 dB for
standard DAS to 5.2 dB for improved DAS, providing 4.4 dB better
performance using the proposed algorithm.
[0082] Looking at all 2D focused images for standard DAS, it can be
observed that clutter strength generally increases closer to skin.
This observation is confirmed when looking at locations of focal
points investigated above. In 3D breast phantom the 2 mm skin layer
has a radius rskin=59 mm. The true tumour response at P.sub.T is
located 35 mm away from the skin (rP.sub.T=24 mm), the strongest
clutter signal at P.sub.1 is 20 mm from the skin (rP.sub.1=39 mm)
and another strong clutter at P.sub.2 is also 20 mm away from the
skin (rP.sub.2=39 mm). As can be seen, all the strong clutter
signals are located closer to skin than the tumour.
[0083] In FIG. 8 curves of cumulative energy collection are
presented for focal points P.sub.T, P.sub.1, P.sub.2. Plots
associated with standard DAS algorithm are shown in FIGS. 8(a),
8(b) and 8(c) for focal points P.sub.T, P.sub.1, P.sub.2,
respectively. The value obtained after summation of all radar
signals is equal to the focused energy F.sub.e in standard DAS.
Next, in the improved DAS algorithm the processor calculates the
standard deviation of energy .sigma..sub.e for all radar signals
and re-calculates energy collection curves by normalising them to
.sigma..sub.e. The resulting normalised curves for locations
P.sub.T, P.sub.1 and P.sub.2 are depicted in FIGS. 8(d), 8(e) and
8(f) (solid curves), respectively.
[0084] It can be observed that, after normalisation, the curves for
P.sub.1, P.sub.2 have significantly dropped compared to P.sub.T,
due to the higher values of standard deviation of the energy
content of the radar signals. Next, the processor performs the
second-order polynomial fitting on the normalised energy collection
curves to obtain the weight factor QF=a. Results of polynomial
fitting are shown as dashed curves in FIGS. 8(d)-8(f). The constant
a associated with x.sup.2 equals a=0.094 for P.sub.T, a=0.01 for
P.sub.i and a=0.049 for P.sub.2. Interestingly, due to a
non-coherent signal summation for focal points P.sub.1 and P.sub.2,
a has not only lower absolute value than for P.sub.T, but has also
negative sign. The focused energy F.sub.e using the improved DAS
algorithm (as in equation 2) will become negative for focal points
where QF=a<0, additionally improving imaging results.
[0085] An alternative arrangement may be obtained by evaluating the
quality factor QF as described in equation (3) below:
QF ( x , y , z ) = .intg. 0 .tau. ( i = 1 M w i ( x , y , z ) y i (
t - T i ( x , y , z ) ) ) 2 t i = 1 M .intg. 0 .tau. ( w i ( x , y
, z ) y i ( t - T i ( x , y , z ) ) ) 2 t ( 3 ) ##EQU00003##
[0086] Thus in this case the quality factor is calculated by
summing the M aligned signals, and generating a first energy data
value E1 from the summed signal:
E 1 = .intg. 0 .tau. ( i = 1 M w i ( x , y , z ) y i ( t - T i ( x
, y , z ) ) ) 2 t ( 4 ) ##EQU00004##
summing the energies of the M aligned signals to generate a second
energy data value E2:
E 2 = i = 1 M .intg. 0 .tau. ( w i ( x , y , z ) y i ( t - T i ( x
, y , z ) ) ) 2 t ( 5 ) ##EQU00005##
and then calculating the ratio E1/E2.
[0087] This quality factor can also be seen to be a measure of the
degree of coherence in the signals and hence yields similar results
to those presented for the improved DAS method above.
[0088] Although the invention has been described above with
reference to one or more preferred embodiments, it will be
appreciated that various changes or modifications may be made
without departing from the scope of the invention as defined in the
appended claims.
* * * * *